IIRC you can get one Alistar skin for free if you do whatever needs to be done on facebook but I don't use social networks so dunno.
And I don't play Alistar. As he's basically a cow.

It's possible some more are also free, but never bothered to check.

But the whole idea of that game is that you can't buy your victory. You can pay for customized looks on a champion you like, but to win, you need to be skilled. And you need a good team, of course.
Just by making things utterly different from WoW milk me monthly fraud and suspicious F2Ps milk me so I can win schemes, today they're making millions on basically a completely free game.